Problem: Simplify the following expression and state the condition under which the simplification is valid: $x = \dfrac{z^2 - 7z}{z^2 + 3z - 70}$
Solution: First factor the expressions in the numerator and denominator. $ \dfrac{z^2 - 7z}{z^2 + 3z - 70} = \dfrac{(z)(z - 7)}{(z + 10)(z - 7)} $ Notice that the term $(z - 7)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(z - 7)$ gives: $x = \dfrac{z}{z + 10}$ Since we divided by $(z - 7)$, $z \neq 7$. $x = \dfrac{z}{z + 10}; \space z \neq 7$